The snowball effect of customer slowdown in critical many-server systems

J. Selen, I.J.B.F. Adan, V.G. Kulkarni, J.S.H. Leeuwaarden, van

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Samenvatting

Customer slowdown describes the phenomenon that a customer's service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient's delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.
Originele taal-2Engels
Uitgeverijs.n.
Aantal pagina's27
StatusGepubliceerd - 2015

Publicatie series

NaamarXiv
Volume1502.02856 [math.PR]

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